It is often desirable to produce objects with radially-varying properties. These objects can be, for example, cylindrical forms made from polymeric materials. The properties which vary radially can include, but are not limited to, index of refraction, color, relative constituent concentrations, thermal expansion coefficient, scattering coefficient, and light absorption coefficient. Prior techniques for radially varying the properties of a cylindrical polymer form, for example, index of refraction, have involved the drawing of a preform made up of polymers with additives, or the addition or extraction of additives into or out of the cylindrical polymer form by, for example, diffusion. These processes impose limits on the possible radial profiles of a property resulting from the physical mechanism used to introduce or extract the additive. Therefore, it can be difficult or even impossible to achieve certain profiles which do not follow from the physics of these processes. One particular cylindrical polymer form for which the radial variation of a material property, namely, the index of refraction, can be critical is a polymer optical fiber. Optical fibers made of optical polymers are often referred to as plastic optical fibers (POFs).
In contrast to the lack of controllability of the radial variation of the index of refraction in POFs, glass, for example, silica, optical fibers have long been produced with well-controlled index of refraction profiles. One form of these glass optical fibers, specifically, single-mode glass optical fibers, have been widely used as long-distance and high-speed communication media due, in part, to low transmission attenuation. However, the small core diameter of the single-mode glass fiber, typically 5 to 10 microns, requires extreme accuracy in the alignment of the fiber for interconnection with other components of the optical communication system. This accurate alignment requirement increases the costs of the whole system. In contrast to single-mode glass fibers, multi-mode glass fibers, which can have diameters larger than single-mode glass fibers, have been used primarily for short-distance transmission such as in local area networks (LANs). However, even their moderate cost for interconnections has limited their application. Consequently, metallic cables such as twisted pair or coaxial cable are still used extensively in short range applications, namely up to 200 meters. However, these metallic cables can not meet the anticipated future bandwidth requirement of several hundred MHz (for example, the asynchronous transfer mode [ATM] standard of 625 megabits per second).
There is considerable interest in developing plastic optical fiber (POF) for use in these short range communication applications, such as LANs. POF can have core diameters of about 0.5 to 1.0 mm, which makes it possible to adopt injection-molded polymer connectors, drastically reducing the cost associated with interconnecting the POF to the other components of a system. These plastic optical fibers can have a step-index structure or a gradient-index structure. Unfortunately, step-index plastic optical fiber (SI-POF) suffers high modal dispersion and therefore cannot meet the bandwidth requirements. However, gradient-index plastic optical fiber (GRIN-POF), having low modal dispersion, shows potential to be a high bandwidth, cost effective solution for use in short range communication applications.
For more than 25 years, POF has been made using a step index (SI) structure in which a core polymer of index n.sub.1 is clad with a polymer of index n.sub.2. The radial dependence of the refractive index is uniform, n.sub.1, out to the core cladding interface, where the index changes discontinuously to the lower value, n.sub.2. A fiber with this structure can transmit data over 100 meters, at the rate of up to several tens of megabits per second. The SI-POF bit rate is limited due to modal dispersion. This rate limit can be extended only slightly by reducing the numerical aperture, or phase space acceptance, of the fiber. The latter approach has been explored where reduction of the numerical aperture from 0.5 to 0.25 increased the bit rate up to 150 megabits per second (Mitsubishi Rayon and Asahi Chemical Industry paper presented to the Third International Conference and Exhibition on Plastic Optical Fibers and Their Applications, Yokohama, Japan, Oct. 26-29, 1994). This bandwidth is not sufficient to meet the growing needs of very high-data-rate, short-distance communications.
A candidate to replace SI fiber for applications requiring fiber lengths up to about 100 meters is GRIN fiber. The theoretical advantage of GRIN fiber is the increased bandwidth (more than one gigabit per second over a 100 meter distance) due to the elimination of modal dispersion. However, the existing production methods for GRIN-POF result in the bandwidth of the fiber being neither stable nor reproducible. Additionally, existing production rates are intrinsically limited by the batch nature of the process and/or the multiple steps of the procedure.
In 1991, an early method of producing GRIN polymer fiber was presented (Koike, Y. et al. [1991] SPIE 1592:62-72). In 1994, experimental results were presented on the measured high-bandwidth of GRIN-POF (two papers presented by researchers at NEC Corp. and Keio University and researchers at IBM, Sandia Nat. Lab., NTT, Fujitsu and Keio University to the Third International Conference and Exhibition on Plastic Optical Fibers and Their Applications, Yokohama, Japan, Oct. 26-29, 1994). Some of the results demonstrated an acceptable bandwidth of 2.5 Gbits/sec over a 100 meter fiber length.
In the last four years, patent applications have been filed on new production processes of GRIN-POF (International Patent PCT WO 92/03750 G02B6/00 Nippon Petrochemical Co.; International Patent PCT WO 92/03751 G02B6/00; Japan Kokai Tokyo Koho JP 03-78706 G02B6/00 Mitsubishi Rayon; Japan Kokai Tokyo Koho JP 04-86603 G02B6/00 Toray Ind.). These processes can be divided into two broad types:
1. Batch processes in which a preform is made with a gradient index and subsequently drawn into a fiber. The preform is made of a polymer(s) plus a low molecular weight additive. PA1 2. Fiber extrusion processes followed by radial extraction of low molecular weight components, and/or radial infusion of low molecular weight components, and subsequent polymerization of residual monomer. The first type of process was successful in producing fiber with the measured high bandwidth of 2.5 Gbits/second referred to earlier. The second type of process has had similar success in achieving an acceptable bandwidth. PA1 (a) the bandwidth is extremely sensitive to the value of g near the optimum value. The curve in the figure is for zero chromatic dispersion in the GRIN fiber. The narrow spectral linewidth (&lt;1 nm) in red Vertical Cavity Surface Emitting Laser (VCSEL) (Lehman, J. A. et al., Fourth International Conference on Plastic Optical Fibers and Applications, p. 31, October 1995, Boston) light approximates this situation, although the bandwidth peak in the figure is somewhat reduced in height, moved slightly, and broadened when dispersion is taken into account (Ishigure et al., supra). PA1 (b) The measured bandwidth data from the batch-processed GRIN fiber is generally a factor of two to three below the theoretical curve for all g and more than one order of magnitude below the theoretical maximum value. PA1 (c) The data is also characterized by a lack of reproducibility for any given value of g. Indeed, there is no evidence from the data of the existence of a maximum in bandwidth at any g value.
With respect to using GRIN-POF in LANs and other related applications, the objective is to minimize modal dispersion. The required radial refractive index profile for minimal modal dispersion has been studied extensively. The model (Halley, P. [1987] Fiber Optic Systems, J. Wiley and Sons; Olshansky, R., D. B. Keck [1976] Appl. Opt. 15(2):483-491) of a GRIN fiber normally considered is that of a "power law" index variation: ##EQU1##
where r is the radial distance from the fiber axis, a is the radius of the fiber, n.sub.1 and n.sub.2 are the refractive indices at r=0 and r=a, respectively, where n.sub.1.gtoreq.n.sub.2. The parameter g controls the index profile as a function of radius and 2.DELTA.=(n.sub.1.sup.2 -n.sub.2.sup.2)/n.sub.1.sup.2. In the particular case where g=2, the power law is called a "parabolic law". This case is close to, but not exactly optimal for maximum bandwidth. It can be shown that if a delta function light pulse is launched into a GRIN fiber, the maximum bandwidth is B where B is given by: ##EQU2##
where L is the length of the fiber, and c is the velocity of light.
Using these equations, we plot the bandwidth (shown in FIG. 1) versus the value of g, and a fixed value of .DELTA.=0.01, which is typical for communications. The important things to be drawn from the graph are:
It is instructive to examine more closely the optimum refractive index profile, characterized by the value of g, versus the magnitude of material dispersion. It has recently been shown that the optimum value of g is changed from about 2 to 2.25 for a spectral line width change from 0 to 2 nm (Ishigure et al., supra). Although the anticipated use of red VCSELs in LANs will probably give a narrower line as mentioned earlier, it is clear that very tight control of the value of g to about .+-.0.05 is required to have optimum performing GRIN fiber in LAN systems.
There are two important considerations in the production of high quality GRIN fiber: stable processing and accurate index profiling. In one of the existing GRIN production processes, the index profile is controlled by differences in diffusion rates of monomers in gel and polymethylmethacrylate(PMMA), monomer relative reactivity rates, and diffusion rate of PMMA molecules into the gel. In another of the existing GRIN production processes, the index gradient profile is again controlled by diffusion rate of monomer out of PMMA fiber and diffusion rate of low index monomer into the PMMA fiber. Other variants of this production process exist and have similar characteristics. The above physical and chemical processes are inherently limited as to the index profiles they can produce, due to the physical and chemical mechanisms involved in the processes. Specifically, not one of the above physical processes is described by mathematical equations which will lead to power law behavior for the refractive index. Therefore, for fundamental physical reasons, the existing batch production processes cannot be expected to produce stable, pure power law behavior for the refractive index profile. For these reasons, existing GRIN-POF production methods result in fiber whose bandwidth is substantially less than theoretically possible, and is not reproducible.